Let a, b and c denote the length of the sides of a right triangle, with c being the length of the hypotenuse. Class 8

Let a, b and c denote the length of the sides of a right triangle, with c being the length of the hypotenuse. Class 8

Question 1.

Let a, b and c denote the length of the sides of a right triangle, with c being the length of the hypotenuse. Find the missing sidelength in each of the following cases: Class 8

(i) a = 5, b = 7

(ii) a = 8, 6 = 12

(iii) a = 9, c = 15

(iv) a = 7, b = 12

(v) a = 1.5, b = 3.5

Solution:

(i) c² = 5² + 7² = 25 + 49 = 74

So, c = [latex]\sqrt{74}[/latex] .

(ii) c² = 8² + 12² = 64 + 144 = 208.

So, c = [latex]\sqrt{208}[/latex] = [latex]4 \sqrt{13}[/latex]

(iii) c² = a² + b² ⇒ 15² = 9² + b²

⇒ 225 = 81 + b² or b² = 225 - 81 = 144

So, b = [latex]\sqrt{144}[/latex]= 12.

(iv) c² = 7² + 12² = 49 + 144 = 193

So, c = [latex]\sqrt{193}[/latex] .

(v) c² = (1.5)² + (3.5)² = 2.25 + 12.25 = 14.50

So, c = [latex]\sqrt{14.50}[/latex] = [latex]5 \sqrt{0.58}[/latex].