Algebra

Rectangle PQRS with PQ = (2x + 8) m and SR = 18 m. PR = 32 m, SQ = _____, x = _____

Step-by-step solution with explanation

Final Answer

, and m

Step-by-step solution

1

Set opposite sides equal to find x

In a rectangle, opposite sides are equal in length. PQ and SR are opposite sides, so we set them equal to each other.
2

Solve the equation for x

Subtract 8 from both sides to get 2x = 10, then divide both sides by 2 to find x = 5.
3

Confirm PQ with x = 5

Plug x = 5 back in to verify PQ = 18 m, which matches SR = 18 m. This confirms x is correct.
4

Recognize diagonals of a rectangle are equal

In any rectangle, the two diagonals are always the same length. So diagonal SQ equals diagonal PR.
5

State the value of SQ

Since PR = 32 m and diagonals of a rectangle are equal, SQ is also 32 m.

Understanding this problem

Learning Insight

Rectangles have two special properties used here: opposite sides are congruent (equal length), and diagonals bisect each other AND are congruent. These properties come from the definition of a rectangle as a parallelogram with right angles.

Quick Tip

Whenever you see a rectangle problem with an unknown side, look for the opposite side — they are always equal. For diagonals, they are always equal in a rectangle, so if you know one, you know both.

Common Mistake

Students often think diagonals of a rectangle bisect each other at right angles (like a rhombus). They bisect each other but NOT necessarily at right angles — that is only true for squares and rhombuses.