Answer:
19 in × 4 in
Explanation:
l - length
w - width
The formula of a perimeter of a rectangle: P = 2(l + w)
The formula of an area of a rectangle: A = lw
We have P = 46in and A = 76in² Substitute:
(1) 2(l + w) = 46
(2) lw = 76
2(l + w) = 46 divide both sides by 2
l + w = 23 subtract w from both sides
l = 23 - w
subtitute it to (2):
(23 - w)w = 76 use the distributive property
23w - w² = 76 subtract 76 from both sides
-w² + 23w - 76 = 0 change the signs
w² - 23w + 76 = 0
w² - 4w - 19w + 76 = 0
w(w - 4) - 19(w - 4) = 0
(w - 4)(w - 19) = 0 ⇔ w - 4 = 0 or w - 19 = 0
w - 4 = 0 add 4 to both sides
w = 4
w - 19 = 0 add 19 to both sides
w = 19
Put the values of w to (1):
l = 23 - 4 = 19 or l = 23 - 19 = 4