Question

7. Three squares have areas of 25 cm2, 16 cm2
and 9 cm2:
(1) Will the squares exactly surround a
right-angled triangle?
(ii) Explain your answer.​

Answer 1

Given:-

• Length of first Square = 25cm²

• Length of Second Square = 16cm²

• Length of third square = 9cm²

To Find :-

• Will the square exactly Surrounds a right - angled triangle.

Formulae used:-

• Area of square = ( Side )²

• Pythogoras theorem =. h² = ( base )² + ( P)²

How to Solve ?

• First we will find the Side of each square.

• Then we will use pythogoras theorem, if the LHS will be equal to RHS.

• From there, we can say that it can surround a Right angled triangle.

Now,

→ Area of 1st Square = ( side )²

→ 25 = ( side )²

→ √25 = √side²

→ side = 5cm.

Again,

→ Area of 2nd Square = ( Side )²

→ √16 = (√ side )²

→ Side = 4cm

Again,

→ Area of 3rd Square = ( Side )²

→ √9 = ( √side )²

→ Side = 3cm

Hence,

using Pythogoras theorem

→ h² = ( base )² + ( P)²

→ (5)² = (4)² + (3)²

→ 25 = 16 + 9

→ 25 = 25.

It's clear that it can surround a right angled triangle.

Answer 2

Given

• Three squares have areas of 25 cm², 16 cm² and 9 cm²

We Find

• Given squares exactly surround a right-angled triangle?

We used

• Area of Square = side²
• Pythagoras theorem = (h)² = (b)² + (p)²

We know that

First we important to know their sides

Area of 1st Square = side²

25 cm² = Side²

Side = √25

side = 5 cm

By, same method we find All sides of Given Squares :-

• 1st Square side = 5 cm

• 2nd Square side = 4 cm

• 3rd Square side = 3 cm

According to the question

We Will check the squares exactly surround a right-angled triangle, so :-

Pythagoras theorem = (h)² = (b)² + (p)²

= (5)² = (4)² + (3)²

= 25 = 16 + 9

= 25 = 25

Hence, this is proved that the squares surround a right-angled triangle.

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