a picture with dimension 10 cm by 8 cm is drawn on a rectangular card leaving a border of uniform width x cm express the area of the border in terms of x
Answers
Step-by-step explanation:
Border Plus Picture equals 198 square centimeters.
Border? Unknown.
Picture: 10%2A17 square centimeters.
Border plus Picture: Let x = the uniform width of border.
%2810%2B2x%29%2817%2B2x%29=198.
Solving for x will allow finding the outside dimensions and the inside dimensions for the frame.
170%2B34x%2B20x%2B4x%5E2=198
34x%2B20x%2B4x%5E2=28
54x%2B4x%5E2=28
2x%5E2%2B27x=14
2x%5E2%2B27x-14=0
x=%28-27%2B-+sqrt%2827%5E2-4%2A2%2A%28-14%29%29%29%2F%282%2A2%29
x=%28-27%2B-+sqrt%28841%29%29%2F%282%2A2%29
x=%28-27%2B-+29%29%2F4, MUST USE PLUS FORM.
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highlight%28x=1%2F2+%2Acm%29
Outside dimensions of the frame, 10.5 cm and 17.5 cm
Answer by MathTherapy(9606) (Show Source): You can put this solution on YOUR website!
A 10cm by 17cm picture is mounted with a border of uniform width on a rectangular frame. If the total area of the border is 198cm^2, find the dimension of the frame.
Dimensions of frame: highlight_green%28highlight_green%2816_by_23%29%29 cm
16_23
Answer:
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Step-by-step explanation:
Let the width of the border be ′x′ inch.
Therefore area of shaded region = (10+2x)(8+2x)−10×8
⇒144=80+20x+16x+4x2−80
⇒4x2+36x−144=0⇒x2+9x−36=0
⇒x2+12x−3x−36=0⇒(x+12)(x−3)=0
∴x=−12,, 3 (neglecting negative value.)
∴ Therefore width of border is 3 inches