Question

Let triangle ABC~triangle DEF.if area of ABC is 100cm2 and area of DEF is 196cm2 and DE=7 then find AB

Answer 1

Solve-are(ABC)/are(DEF)=(AB)^2/(DE)^2
100/196=AB^2/7^2
10/14=AB/7
70=14AB
AB=70/14
AB=5 Answer

Answer 2

Answer:

5 cm

Step-by-step explanation:

Given : ΔABC≈ΔDEF

To Find :If area of ABC is 100 sq.cm and area of DEF is 196 sq.cm. and DE=7 then find AB

Solution:

Area of ΔABC is 100 sq.cm.

Area of ΔDEF is 196 sq.cm.

Since we are given that ΔABC≈ΔDEF

Property : The ratio of areas of two similar triangles is proportional to the squares of the corresponding sides of both the triangles.

So, $\frac{\text{Area of triangle}ACB}{\text{Area of triangle}DFE} =\frac{AB^2}{DE^2}$

$\frac{100}{196} =\frac{AB^2}{7^2}$

$\frac{100}{196} =\frac{AB^2}{49}$

$\frac{100 \times 49}{196} =AB^2$

$25 =AB^2$

$\sqrt{25} =AB$

$5=AB$

Hence the length of AB is 5 cm