Question

Jerome found the lengths of each side of triangle QRS as shown, but did not simplify his answers. Simplify the lengths of each side to answer the question. Which statement about triangle QRS is true?

a. Triangle QRS is an equilateral triangle because QR = RS.

b. Triangle QRS is an isosceles triangle because QR = QS.

c. Triangle QRS is a scalene triangle because all sides have different lengths.

d. Triangle QRS is an isosceles triangle because QR = RS.

Answer 1

D. Triangle QRS is an isosceles triangle because QR = RS.

Explanation:

Find the length of each side of the triangle using the formula for calculating the distance between two points.

D = √(x2-x1)²+(y2-y1)²

For side RS

R(0,0) and S(5, -3.322)

RS = √(5-0)²+(-3.322-0)²

RS = √25+11.035684

RS = √36.035684

RS = 6.0029

For side RQ

R(0,0) and Q(-3, -5.2)

RQ = √(-3-0)²+(-5.2-0)²

RQ = √9+27.04

RQ = √36.04

RQ = 6.0033

For side QS

Q(-3,-5.2) and S(5, -3.322)

QS = √(5+3)²+(-3.322+5.2)²

QS = √64+3.526884

QS = √67.526884

QS = 8.22

From the calculation it can be seen that RS=QR

Since the two sides f the triangle are equal, hence the triangle is an isosceles triangle. An isosceles triangle is a triangle that has two of its sides equal