# The length of the base of an isosceles triangle is x. The length of a leg is 2x - 6. The perimeter is 53. Find x. Question
Right triangles and trigonometry The length of the base of an isosceles triangle is x. The length of a leg is 2x - 6. The perimeter is 53. Find x. 2021-01-17
The legs of an isosceles triangle are congruent. Since the perimeter is the sum of the three side lengths, we write:
x+(2x−6)+(2x−6)=53
Solve for x: 5x−12=53
5x=65
$$\displaystyle{x}=\frac{{65}}{{5}}$$
x=13

### Relevant Questions Find the length of a leg of an isosceles right triangle whose hypotenuse has length 12 Use function notation to describe the way the second variable (DV) depends upon the first variable (IV). Determine the domain and range for each, determine if there is a positive, negative, or no relationship, and explain your answers.
A)IV: an acute angle V in a right triangle: DV: the area B of the triangle if the hypotenuse is a fixed length G.
B)IV: one leg P of a right triangle: DV: the hypotenuse G of the right triangle if the other leg is 2
C)IV: the hypotenuse G of a right triangle: DV: the other leg P of the right triangle is one leg is 5. Expanding isosceles triangle The legs of an isosceles right tri- angle increase in length at a rate of 2 m/s.
a. At what rate is the area of the triangle changing when the legs are 2 m long?
b. At what rate is the area of the triangle changing when the hypot- enuse is 1 m long?
c. At what rate is the length of the hypotenuse changing? Expanding isosceles triangle The legs of an isosceles right tri- angle increase in length at a rate of 2 m/s.
a. At what rate is the area of the triangle changing when the legs are 2 m long?
b. At what rate is the area of the triangle changing when the hypot- enuse is 1 m long?
c. At what rate is the length of the hypotenuse changing? Expanding isosceles triangle The legs of an isosceles right tri- angle increase in length at a rate of 2 m/s.
a. At what rate is the area of the triangle changing when the legs are 2 m long?
b. At what rate is the area of the triangle changing when the hypot- enuse is 1 m long?
c. At what rate is the length of the hypotenuse changing? A rectangle with dimensions 21.6 × 12 has a right triangle with a base 9.6 and a height of 7.2 cut out of the rectangle. What is the area of the shaded region?    