Maths-
General
Easy

Question

Use △ ABC, where M, N, Q are midpoints of the sides.
MQ = 3y − 5, AC = 4y + 2

hintHint:

Use triangle midsegment theorem.

The correct answer is: MQ = 13 and AC = 26


    Complete step by step solution:
    A midsegment of a triangle is a segment that connects the midpoints of two sides of
    a triangle. Its length is always half the length of the 3rd side of the triangle.
    Here, MQ is parallel to AC and M Q equals 1 half A C

    text  So,  end text 3 y minus 5 equals 1 half left parenthesis 4 y plus 2 right parenthesis

    not stretchy rightwards double arrow 3 y minus 5 equals 1 half cross times 2 left parenthesis 2 y plus 1 right parenthesis

    not stretchy rightwards double arrow 3 y minus 5 equals 2 y plus 1

    not stretchy rightwards double arrow 3 y minus 2 y equals 1 plus 5
    not stretchy rightwards double arrow y equals 6
    Now, MQ = 3y - 5 = 3 × 6 - 5=13 and AC = 4y + 2 = 4 × 6 + 2 = 26.

    Related Questions to study

    General
    Maths-

    M and N are midpoints of the sides AB and AC respectively.
    Which of the given statements is NOT correct?

    M and N are midpoints of the sides AB and AC respectively.
    Which of the given statements is NOT correct?

    Maths-General
    General
    Maths-

    Use △ ABC, where M, N, Q are midpoints of the sides.
    MN = 3x + 8, BC = 2x + 24
     

    Use △ ABC, where M, N, Q are midpoints of the sides.
    MN = 3x + 8, BC = 2x + 24
     

    Maths-General
    General
    Maths-

    Place the figure in a coordinate plane in a convenient way.
    Assign coordinates to each vertex.
    Right triangle: leg lengths are a and b.

    Place the figure in a coordinate plane in a convenient way.
    Assign coordinates to each vertex.
    Right triangle: leg lengths are a and b.

    Maths-General
    parallel
    General
    Maths-

    Place the figure in a coordinate plane in a convenient way.
    Assign coordinates to each vertex.
    Rectangle: length is l and width is b.

    Place the figure in a coordinate plane in a convenient way.
    Assign coordinates to each vertex.
    Rectangle: length is l and width is b.

    Maths-General
    General
    Maths-

    Place the figure in a coordinate plane in a convenient way.
    Assign coordinates to each vertex.
    Square: side length is 4.

    Place the figure in a coordinate plane in a convenient way.
    Assign coordinates to each vertex.
    Square: side length is 4.

    Maths-General
    General
    Maths-

    Place the figure in a coordinate plane in a convenient way. Assign coordinates to each vertex. Isosceles right triangle: leg length is 5 units.

    Place the figure in a coordinate plane in a convenient way. Assign coordinates to each vertex. Isosceles right triangle: leg length is 5 units.

    Maths-General
    parallel
    General
    Maths-

    Place the figure in a coordinate plane in a convenient way.
    Assign coordinates to each vertex. Right triangle: leg lengths are 3 units and 4 units.

    Place the figure in a coordinate plane in a convenient way.
    Assign coordinates to each vertex. Right triangle: leg lengths are 3 units and 4 units.

    Maths-General
    General
    Maths-

    Salim wants to purchase tickets from a vendor to watch a tennis match. The vendor charges a one-time service fee for processing the purchase of the tickets. The equation  T = 15n +2 represents the total amount T , in dollars, Salim will pay for  tickets. What does 12 represent in the equation?

    Salim wants to purchase tickets from a vendor to watch a tennis match. The vendor charges a one-time service fee for processing the purchase of the tickets. The equation  T = 15n +2 represents the total amount T , in dollars, Salim will pay for  tickets. What does 12 represent in the equation?

    Maths-General
    General
    Maths-

    In △ PQR, DE is the midsegment.
    Find the value of x and the length of side PQ.

    In △ PQR, DE is the midsegment.
    Find the value of x and the length of side PQ.

    Maths-General
    parallel
    General
    Maths-

    In△ ABC, AN = BN, BM = MC
    Find AC.

    In△ ABC, AN = BN, BM = MC
    Find AC.

    Maths-General
    General
    Maths-

    The segment connecting the midpoints of two sides of a
    triangle is

    The segment connecting the midpoints of two sides of a
    triangle is

    Maths-General
    General
    Maths-

    The segment connecting the midpoints of two sides of a
    triangle is

    The segment connecting the midpoints of two sides of a
    triangle is

    Maths-General
    parallel
    General
    Maths-

    Every triangle has ___ mid-segments.

    Every triangle has ___ mid-segments.

    Maths-General
    General
    Maths-

    The simple interest on a fixed deposit of Rs. 4600 at the rate of 13% p.a. is Rs.3588. Find the term of the deposit.

    The simple interest on a fixed deposit of Rs. 4600 at the rate of 13% p.a. is Rs.3588. Find the term of the deposit.

    Maths-General
    General
    Maths-

    Ram borrowed Rs. 24000 from a bank for 3 years at the rate of 12% interest. Find the amount due from him after 3 years.

    Ram borrowed Rs. 24000 from a bank for 3 years at the rate of 12% interest. Find the amount due from him after 3 years.

    Maths-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.