(2) The triangle has an area of 7 & 7/8 cm2 and a base of 5 & 1/4 cm. What is the
2 answers:
Answer:
h = 3 cm
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = bh ( b is the base and h the height )
Here A = 7 =
← expressed as an improper fraction
and b = 5 =
, thus
×
× h =
, that is
h =
Multiply both sides by 8 to clear the fractions
21h = 63 ( divide both sides by 21 )
h = 3
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Question: What value of c will complete the square below () and make the expression a perfect square trinomial?
Answer: c = 225
Step-by-step explanation:
Perfect square trinomials come in the form a² + 2ab + b², which is equal to (a + b)². In the presented trinomial, we can immediately identify that <u>a = x, and b² = c</u>, but we need to find the numerical value of .
To do this, note that the middle term, or <u>2ab, corresponds with (is equal to) 30x</u>. We know that a = x, and thus, <u>2ab = 2bx</u>. Now, 2bx and 30x are corresponding terms; thus, <u>2bx = 30x</u>.
Dividing by on both sides gives us <u>b = 15</u>. Therefore, c = b² = 15² = 225. (As a squared binomial, this would be (x + 15)² as a = x and b = 15.)