Practice Quiz

SAT Math

Category - Geometry and Measurement

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What is the perimeter of the triangle in the figure below?
  1. 30
  2. 35
  3. 40
  4. 45
  5. 50
Explanation
Answer: A - The perimeter of the triangle is 30. Apply the Pythagorean Theorem and solve for x.
(x+1)^2=x^2+(x-7)^2
x^2+2x+1=x^2+x^2-14x+49
x^2-16x+48=0
x^2-16x+48=x^2-12x-4x+48=x(x-12)-4(x-12)=(x-12)(x-4)
(x-12)(x-4)=0⟹x=12∨x=4

A side can’t be negative, so x = 12.
P=x-7+x+x+1=3x-6=3×12-6=36-6=30
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