Mathias was asked whether the following equation is an identity:
2 answers:
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<u>Complete Question:</u>
Janeel has a 10 inch by 12 inch photograph. She wants to scan the photograph, then reduce the results by the same amount in each dimension to post on her Web site. Janeel wants the area of the image to be one eight of the original photograph. Write an equation to represent the area of the reduced image. Find the dimensions of the reduced image.
<u>Correct Answer:</u>
A)
B) Dimensions are : Length = 10-x = 3 inch , Breadth = 12-x = 5 inch
<u>Step-by-step explanation:</u>
a. Write an equation to represent the area of the reduced image.
Let the reduced dimensions is by x , So the new dimensions are
According to question , Area of new image is :
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So the equation will be :
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b. Find the dimensions of the reduced image
Let's solve :
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By Quadratic formula :
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x = 15 is rejected ! as 15 > 10 ! Side can't be negative
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Therefore, Dimensions are : Length = 10-x = 3 inch , Breadth = 12-x = 5 inch
Answer:
(,
) = (30, 16)
Step-by-step explanation:
First find the similarity
Since you know the legnth of the hypotenuse (the longest one) for both traingles, you can find the similarity by dividing the longer by the shorter:
50 ÷ 20 = 2.5
The similarity between the 2 triangles is 2.5.
Now find the length of on the longer one, use the shorter one's length and the similarity:
12 × 2.5 = 30
So the length of is equal to 30
Now lets find , lets use the length of the larger triangle this time and divide the length of the longer leg (there are 2 legs in every triangle, if you don't know the hypotenus's length, use the pythagorean theorem) and divide it by the similarity:
40 ÷ 2.5 = 16
= 16
WooHoo! (,
) = (30, 16)