Question

A right triangle has an area of 98 square inches. If the triangle is not an Isosceles triangle, what are the all possible lengths of the legs?

Answer 1

The possible length of the triangle =

1) (1inches, 196inches)

2) (2incheq, 98inches)

3) (4inches , 49 inches)

4) (7 inches , 28 inches)

Explanation:

We are told the above Triangle is not an Isosceles Triangle

Hence, we assume it is a right angle triangle

The area of a triangle is = 1/2 × Base × Height

= let us represent Base and Height = x

Hence:

1/2 × x × x = 98

x² /2 = 98

Cross Multiply

x² = 98 × 2

x² = 196

Step 2

We find the factors of 196

1× 196 = 196 (1, 196)

2 × 98 = 196 (2, 98)

4 ×49 = 196 (4, 49)

7 × 28 = 196 (7, 28)

Therefore, all the possible length of the triangle =

1) (1inches, 196inches)

2) (2incheq, 98inches)

3) (4inches , 49 inches)

4) (7 inches , 28 inches)