Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

In ∆ABC, ∠ABC = 90° AD is the median to BC and CE is the median to AB. If AC = 5 cm and AD = $fraction numerator 3 square root of 5 over denominator 2 end fraction$ cm, find CE.

hint Hint:

Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.
If a is the perpendicular, b is the base, and c is the hypotenuse, then according to the definition, the Pythagoras Theorem formula is given as
c2= a2 + b2

The correct answer is: Hence, the value of CE is 2√5 cm.

It is given that AD is the median to BC. So, BD = CD. It is also given that CE is the median to AB. So, AE = BE
Also, AC = 5 cm and AD = $fraction numerator 3 square root of 5 over denominator 2 end fraction$ cm
Applying Pythagoras theorem in △ABD
AD² = BD² + AB²
$AD squared equals open parentheses fraction numerator B C over denominator 2 end fraction close parentheses squared plus AB squared$
$AD squared equals 1 fourth BC squared plus AB squared$
Applying Pythagoras theorem in △BCE
CE² = BE² + BC²
$CE squared equals 1 fourth AB squared plus BC squared$
Adding equations (1) and (2)
$A D squared plus C E squared equals 1 fourth B C squared plus A B squared plus 1 fourth A B squared plus B C squared$
$A D squared plus C E squared equals 5 over 4 open parentheses A B squared plus B C squared close parentheses$
As △ABD is a right-angled triangle. So AB² + BC²= AC²
$A D squared plus C E squared equals 5 over 4 A C squared$
$open parentheses fraction numerator 3 square root of 5 over denominator 2 end fraction close parentheses squared plus C E squared equals 5 over 4 cross times 5 squared$
$C E squared equals 125 over 4 minus 45 over 4 equals 20$
$CE equals square root of 20 equals 2 square root of 5 cm$
final answer:
$text Hence, the value of CE is end text 2 square root of 5 cm text . end text$

Related Questions to study

Find the vertex, axis of symmetry and sketch the graph of the function
f(x)= x²+2

Find the vertex, axis of symmetry and sketch the graph of the function
f(x)= x²+2

Find the vertex, axis of symmetry and sketch the graph of the function f(x)= x² -5

Find the vertex, axis of symmetry and sketch the graph of the function f(x)= x² -5

Find the vertex, axis of symmetry and sketch the graph of the function g(x)= x² -1

Find the vertex, axis of symmetry and sketch the graph of the function g(x)= x² -1

parallel

Find the vertex, axis of symmetry and sketch the graph of the function h(x)= x²+0.5

Find the vertex, axis of symmetry and sketch the graph of the function h(x)= x²+0.5

Find the vertex, axis of symmetry and sketch the graph of the function.
F(x) = -2(x + 1)² + 5

Find the vertex, axis of symmetry and sketch the graph of the function.
F(x) = -2(x + 1)² + 5

Find the vertex, axis of symmetry and sketch the graph of the function f(x)= x²-2.25

Find the vertex, axis of symmetry and sketch the graph of the function f(x)= x²-2.25

parallel

Find the vertex, axis of symmetry and sketch the graph of the function f(x)= x²+50

Find the vertex, axis of symmetry and sketch the graph of the function f(x)= x²+50

Solve Graphically :
X+Y= -1
Y-2X=-4

Solve Graphically :
X+Y= -1
Y-2X=-4

Find the vertex, axis of symmetry and sketch the graph of the function h(x)= x²+7

Find the vertex, axis of symmetry and sketch the graph of the function h(x)= x²+7

parallel

The sides of a right-angled triangle are 2x – 1, 2x, 2x + 1. Find x.

The sides of a right-angled triangle are 2x – 1, 2x, 2x + 1. Find x.

How does the graph of f(x) = -3(x - 5)²+ 7 compare to the graph of the parent function

How does the graph of f(x) = -3(x - 5)²+ 7 compare to the graph of the parent function

Find the vertex, axis of symmetry and sketch the graph of the function g(x)= (x-1)²

Find the vertex, axis of symmetry and sketch the graph of the function g(x)= (x-1)²

parallel

Find Graphically the vertices of the triangle whose sides have equations 2Y-X=8 , 5Y-X= 14 and Y-2X=1 respectively. Take 1 cm = 1 unit on both the axes.

Find Graphically the vertices of the triangle whose sides have equations 2Y-X=8 , 5Y-X= 14 and Y-2X=1 respectively. Take 1 cm = 1 unit on both the axes.

Find the vertex, axis of symmetry and sketch the graph of the function g(x)= (x+2)²

Find the vertex, axis of symmetry and sketch the graph of the function g(x)= (x+2)²

Find the vertex, axis of symmetry and sketch the graph of the function h(x)= (x-6)²

Find the vertex, axis of symmetry and sketch the graph of the function h(x)= (x-6)²

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.