Question

Two corresponding sides of similar triangles are 2 cm and 5 cm. What is the area of the second triangle if the area of the first triangle is 8 cm2?
The triangles ABC and DFG are similar and the ratio of their corresponding sides is 6:5. The area of the triangle ABC is greater than the area of the triangle DFG by 77 cm2. Find the areas of these triangles.

Answer 1

Answer:

(1) Area of second triangle= 50 cm^2.

(2) Area of ΔABC=98 cm^2.

   and Area of ΔDFG=175 cm^2.

Step-by-step explanation:

" For two similar triangles the ratio of sides is equal to the ratio of square of their areas".

i.e. if a,b are the corresponding sides of two similar triangles and let A and B denote the area of two triangles then we have the relation as:

$\dfrac{a^2}{b^2}=\dfrac{A}{B}$

(1)

for the first question:

we have a=2, b=5.

A=8 cm^2.

Hence,

$\dfrac{2^2}{5^2}=\dfrac{8}{B}\\\\\dfrac{4}{25}=\dfrac{8}{B}$

B=50 cm^2.

Hence, the area of second triangle is 50 cm^2.

(2)

In second option we have:

a=6 and b=5.

A-B=77 cm^2.

A=77+B

$\dfrac{6^2}{5^2}=\dfrac{A}{B}\\ \\\dfrac{36}{25}=\dfrac{77+B}{B}\\ \\36B=25\times77+25B\\\\36B-25B=25\times77\\\\11B=25\times77\\\\B=25\times7\\\\B=175$

Hence area of second triangle i.e. ΔDFG is 175 cm^2.

and area of first triangle i.e. ΔABC=175-77=98 cm^2.