Question

If the area of a right triangle is 70 cm² and one of the sides containing the right angle is 14 cm. Find the length of other leg.​

Answer 1

Answer :

›»› The length of other leg or height of right angle triangle is 10 cm.

Step-by-step explanation :

Given :

• Area of right angle triangle = 70 cm².
• One side or base of a right angle triangle = 14 cm.

To Find :

• Length of other leg or height of a right angle triangle = ?

Formula required :

To find the length of other leg or height of a right angle triangle we use the formula of area of triangle.

Formula of area of triangle to calculate the length of other leg or height of a right angle triangle is given by,

→ Area of triangle = 1/2 × b × h.

Here,

• b is the Base of right angle triangle.
• h is the Height of right angle triangle.

Units,

• The unit of base is centimetres (cm).
• The unit of height is centimetre (cm).

Solution :

Let us assume that, the length of other leg or height of a right angle triangle is h cm.

We know that, if we are given with the area of triangle and base of triangle then we have the required formula, that is,

→ Area of triangle = 1/2 × b × h.

By using the formula of area of triangle to calculate the length of other leg or height of a right angle triangle and substituting all the given values in the formula, we get :

→ 70 = 1/2 × 14 × h

→ 70 = 1 × 7 × h

→ 70 = 7 × h

→ 70 = 7h

→ 7h = 70

→ h = 70/7

→ h = 10

Hence, the length of other leg or height of right angle triangle is 10 cm.

Answer 2

Answer:

Given :-

• The area of a right angled triangle is 70 cm² and the one side containing the right angle is 14 cm.

To Find :-

• What is the length of other length or the height of a right angled triangle.

Formula Used :-

★ Area = ½ × Base × Height ★

Solution :-

Let, the height be h

Given :

• Area = 70 cm²
• Base = 14 cm

According to the question by using the formula we get,

⇒ Area = ½ × Base × Height

⇒ 70 = ½ × 14 × h

⇒ 70 = 7 × h

⇒ 70 ÷ 7 = h

⇒ 10 = h

➠ h = 10 cm

∴ The other length or the height of a right angled triangle is 10 cm .

Let's Verify :-

↦ Area = ½ × Base × Height

↦ 70 = ½ × 14 × h

Put h = 10 we get,

↦ 70 = ½ × 14 × 10

↦ 70 = 7 × 10

↦ 70 = 70

➦ LHS = RHS

Hence, Verified ✔