Question

triangle ABC congruent triangle DEF if area of triangle ABC is 50 cm square then ,find the area of triangle DEF​

Answer 1

Answer:

5cm

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}Area of triangleDFEArea of triangleACB=DE2AB2

\frac{100}{196} =\frac{AB^2}{7^2}196100=72AB2

\frac{100}{196} =\frac{AB^2}{49}196100=49AB2

\frac{100 \times 49}{196} =AB^2196100×49=AB2

25 =AB^225=AB2

\sqrt{25} =AB25=AB

5=AB5=AB

Hence the length of AB is 5 cm

Answer 2

The area of the triangle DEF = 50 cm square.

Explanation:

We know that if two triangles are congruent then

a. Corresponding sides are equal.

b. Corresponding angle are equal.

c. Area of both triangles are equal.

Given : Triangle ABC congruent triangle DEF .

⇒ Area of Triangle ABC = Area of Triangle DEF

If area of triangle ABC is 50 cm square.

⇒Area of Triangle DEF = 50 cm square.

Hence, the area of the triangle DEF = 50 cm square.

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