University:
Morehouse College
Course:
HMTH 105 | College Algebra 1
Academic year:

2024
Views:

378

Pages:

2
Author:

Reynaldo Wong

Question 1 The length of the base of an isosceles triangle is 𝑥 x. The length of a leg is 2 𝑥 − 6 2x−6. The perimeter is 53. Find 𝑥 x. Answer 1 An isosceles triangle has congruent legs. The perimeter is the product of the lengths of the three sides, therefore we write: 𝑥 + ( 2 𝑥 − 6 ) + ( 2 𝑥 − 6 ) = 53 x+(2x−6)+(2x−6)=53 Solve for 𝑥 x: 5 𝑥 − 12 = 535 𝑥 = 65 𝑥 = 65 5 𝑥 = 13 5x−12=535x=65x= 5 65 x=13 Question 2 The triominoes shown are pieces from a game. Classify the shape of a triomino by its sides and angles. What is the measure of the largest angle? How many sides are congruent? Answer 1 A triomino has three sides, so it is a triangle. The largest angle is 6 0 ∘ 60 ∘ . In fact, all angles measure 6 0 ∘ 60 ∘ . All three sides are congruent. Hence, a triomino is an equilateral triangle. Question 3 Triangle DEF is shown below. What is the measure of ∠ 𝐷 ∠D? Answer 1 The sum of the angle measures of a triangle is 18 0 ∘ 180 ∘ . So, we write: 𝑚 ∠ 𝐷 + 𝑚 ∠ 𝐸 + 𝑚 ∠ 𝐹 = 18 0 ∘ m∠D+m∠E+m∠F=180 ∘ 𝑚 ∠ 𝐷 + 5 7 ∘ + 3 9 ∘ = 18 0 ∘ m∠D+57 ∘ +39 ∘ =180 ∘ 𝑚 ∠ 𝐷 + 9 6 ∘ = 18 0 ∘ m∠D+96 ∘ =180 ∘ 𝑚 ∠ 𝐷 = 8 4 ∘ m∠D=84 ∘ Question 4 The lengths of the diagonals of a rectangle are represented by 8 𝑥 + 3 feet 8x+3feet and 4 𝑥 + 7 feet 4x+7feet. Find the length of each diagonal. Answer 1 The diagonals of a rectangle are congruent, so we can set the expressions equal to each other and solve for 𝑥 x: 8 𝑥 + 3 = 4 𝑥 + 7 8x+3=4x+7 8 𝑥 − 4 𝑥 = 7 − 3 8x−4x=7−3 4 𝑥 = 4 𝑥 = 1 4x=4x=1 Using either expression, each diagonal measures: 8 ( 1 ) + 3 = 11 feet 8(1)+3=11feet Question 5 In △ 𝑃 𝑄 𝑅 △PQR, identify the hypotenuse, adjacent leg, and opposite leg for ∠ 𝑅 ∠R. Answer 1 The hypotenuse is the longest side and is opposite the right angle: 𝑃 𝑅 PR. The adjacent leg for ∠ 𝑅 ∠R is the leg where 𝑅 R is one of the endpoints: 𝑄 𝑅 QR. The opposite leg for ∠ 𝑅 ∠R is the leg opposite 𝑅 R: 𝑃 𝑄 PQ.