Question

two triangle are similar. the length of one of the tiangle are 2 times that of the other. the area of the smaller triangle are 25cm^2. Find The Larger Triangl?​

Answer 1

Answer:

corresponding side of larger triangle = 10 cm and area = 100cm²

let the larger ∆ be ∆PQR and smaller be ∆ ABC.

length of side of ∆ABC = l

length of side of ∆PQR = 2l

we know, ratio of area of two similar triangles are proportional to ratio of square of their sides. so,

ar.∆ABC/AR.∆PQR = l²/(2l)²

=> 25/ ar.∆PQR = l²/4l²

=> 25× 4l² / l² = ar. ∆ PQR

=> 100cm² = ar.∆PQR

=> side corresponding = √100= 10 cm

Answer 2

GivEn:

• The length of one of the tiangle is 2 times that of the other.
• The area of the smaller triangle is 25cm².

To find:

• The Larger Triangle?

Solution:

☯ Let length of third side be x cm.

We know that,

★ Ratio of the areas of two similar triangles is equal to the ratio of the square of their corresponding sides.

Here,

• Larger triangle = ∆PQR
• Smaller triangle = ∆ABC
• Sides of both triangles = x,2x

Therefore,

⇒ 25/∆PQR = (x)²/(2x)²

• Area of triangle = 2 × a. So, x²,4x²

⇒ ∆PQR = 25 × 4x²/x²

⇒ ∆PQR = 100x²/x²

⇒ ∆PQR = 100 cm

∴ Hence, Area of the larger triangle is 100cm.

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More to know:

• Area of triangle = ½ × base × height

• Heron's Formula = √s(s - a)(s - b)(s - c)

• Sum of all angles of a triangle is 180°.