GRE-Math-Questions-to-Know-by-Test-Day-2nd-Edition_pag202

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Answers ‹ 193
210. 14 Sketch a figure. The perimeter, P, is P = +l w2 2 , where the rectangle’s length, l, 
is AD = BC, and its width, w, is AB = DC. Write and solve simultaneously the following 
two equations (assuming throughout that l and w are positive measures):
A
B C
D
 (1) =lw 12 and (2) = +l w52 2 2 (by the Pythagorean theorem)
 Solve (2) for w: w = − l25 2 .
 Substitute into (1): − =l l25 122 .
 Square both sides: − =l l(25 ) 1442 2 .
 Simplify: − + =l l25 144 04 2 .
 Factor as you would a quadratic: − −l l( 9)( 16)2 2 .
 Keeping in mind that l is positive, then from these two equations, l = 3 with w = 4 or 
l = 4 with w = 3. Either way, P = +l w2 2 = 14.
211. 5 The area of a square with sides of length, s, is s2. The area of a parallelogram with 
base, b, and height, h, is bh. Write and solve the following equation:
 = h10 202
 = h100 20
 h = 5
212. 11
33
 the measure of RCQ PCSthe measure of 120∠ = ∠ = ° (vertical angles are congru-
ent). Thus, ⋅ °
°
= °
°
=2 120
360
240
360
2
3
 of the circle is not shaded. Hence, 1
3
 of the circle is shaded.
213. 64 Note: In the following discussion, m immediately preceding an angle means “the 
measure of” the angle. ∠ = ∠ = °m A m DEB 58 (corresponding angles of parallel lines are 
congruent). Because ≅BD DE , triangle BDE is isosceles. Thus, ∠ = ∠ = °m B m DEB 58 (base 
angles of an isosceles triangle are congruent). Thus, ∠ = ° − ° = °m C 180 2(58 ) 64 .
06_McCune_Answer.indd 193 2/21/22 4:48 PM