Given ΔABC ~ ΔDEF and their areas are 196sq cm and 225 sqcm respectively . If AB = 7cm then find DE
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Answer:
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}
Area of triangleDFE
Area of triangleACB
=
DE
2
AB
2
\frac{100}{196} =\frac{AB^2}{7^2}
196
100
=
7
2
AB
2
\frac{100}{196} =\frac{AB^2}{49}
196
100
=
49
AB
2
\frac{100 \times 49}{196} =AB^2
196
100×49
=AB
2
25 =AB^225=AB
2
\sqrt{25} =AB
25
=AB
5=AB5=AB
Hence the length of AB is 5 cm
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