The table shows the relationship between a𝑎, the area of a rectangle, and hℎ, its height, when the base remains constant.Which equation represents the relationship between hℎ and a𝑎? a=2h+4𝑎=2ℎ+4 a=3h+2𝑎=3ℎ+2 a=4h𝑎=4ℎ a=h+6𝑎=ℎ+6
Question
The table shows the relationship between a𝑎, the area of a rectangle, and hℎ, its height, when the base remains constant.Which equation represents the relationship between hℎ and a𝑎? a=2h+4𝑎=2ℎ+4 a=3h+2𝑎=3ℎ+2 a=4h𝑎=4ℎ a=h+6𝑎=ℎ+6
Solution
The area of a rectangle is given by the formula a = bh, where a is the area, b is the base, and h is the height. Since the base is constant in this case, we can represent the base as a constant value, k. Therefore, the equation becomes a = kh.
Looking at the options given:
a = 2h + 4 a = 3h + 2 a = 4h a = h + 6
The only equation that fits the form a = kh (where k is a constant) is a = 4h. Therefore, the equation that represents the relationship between h and a when the base remains constant is a = 4h.
Similar Questions
A triangle has a base of 24 inches and an area of 260 square inches. Which equation can be used to find h, the height of the triangle?ResponsesA 24h = 26024 h = 260B 12h = 26012 h = 260C 48h = 26048 h = 260D 260h = 12260 h = 12
The diagram shows a right-angled triangle and a rectangle.The area of the triangle is twice the area of the rectangle.Given that ◂⋅▸=◂⋅▸, find the area of the rectangle.Input note: give your answer correct to 2 decimal places.(5 marks)
If a rectangle has a length of (2x−3)(2𝑥−3) and a width of (2x+3)(2𝑥+3) , what is the area of the rectangle? Write your answer in standard form.
A rectangular prism has a volume of 900 cubic units. The prism has a length of 25 units and a width of 12 units. Which equation could be used to find h, the height of the prism?ResponsesA 150h = 900150 h = 900B 300h = 900300 h = 900C 18.5h = 90018.5 h = 900D 37h = 900
Suppose that △𝑃𝑄𝑅 has an area of A square inches and that the vertices of △𝑆𝑇𝑈 are the midpoints of the sides of △𝑃𝑄𝑅. In terms of A, what is the area of △𝑆𝑇𝑈 in square inches?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.