Question

The legs of a right triangle are in the ratio of 3:4 and it's area is 1014sq.cm find the sides and it's perimeter

Answer 1

Answer:

sides: 39, 52, 65.

perimeter: 156

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finding the length of the legs:

we will first find the length of the legs of the right angled triangle, when their measurements are 3n and 4n respectively, when n is the unknown number multiplied by the terms of the ratio.

now, we will use the following equation to find the length of the legs.

area = leg1 x leg2 x 1/2

now, we replace the variables given with the values we have.

1014 = 3n x 4n x 1/2

now, we simplify this.

1014 = 12n²/2

1014 = 6n²

1014/6 = n²

169 = n²

n = √169

n = 13

(leg1) 3n = 39

(leg2) 4n = 52

so, the sides are 39 and 52.

finding the perimeter

to find the perimeter, we must first find out the hypotenuse of the right angled triangle.

to find that, we will use the formula: a²+b²=c²

we will take the hypotenuse as c.

c² = 39² + 52²

c² = 4225

c = 65

now, we find the perimeter.

the perimeter is the sum of all the sides:

39 + 52 + 65

= 156